derivative of a+bx+cx^2+dx^3

Lösung

\frac{d}{d x} (a + b x + c x^{2} + d x^{3})

3 d x^{2} + 2 c x + b

Schritte zur Lösung

\frac{d}{d x} (a + b x + c x^{2} + d x^{3})

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d a}{d x} + \frac{d}{d x} (b x) + \frac{d}{d x} (c x^{2}) + \frac{d}{d x} (d x^{3})

\frac{d a}{d x} = 0

\frac{d}{d x} (b x) = b

\frac{d}{d x} (c x^{2}) = 2 c x

\frac{d}{d x} (d x^{3}) = 3 d x^{2}

= 0 + b + 2 c x + 3 d x^{2}

Vereinfache

= 3 d x^{2} + 2 c x + b

\frac{\partial}{\partial y} (\frac{13}{2} x^{4} y)

\int \frac{ln ( sin ( x ) )}{sin ^{2} ( x )} d x

\frac{\partial}{\partial x} (x^{2} + y^{2} - y^{2} x - 7)

t an g e n t f (x) = x^{2} - 2, (3, 7)

x \to 0 lim ((c e^{x} + 1) i f)